Nina Arianda’s performance as Billie Dawn, the deceptive ditz who’s the driving force of Garson Kanin’s comedy Born Yesterday, is not notable for being this young actress’s stunning New York debut. That came Off-Broadway last year, as Vanda in David Ives’s Venus in Fur. It is, however, important for proving that this glimmering performer is not merely a flash in the pan. With this sexy and sophisticated, and thoroughly different and completely disarming, performance, she reveals herself the kind of natural, and naturally gifted, stage actress we’re constantly told the theatre can no longer produce. Yet go to the Cort, where Doug Hughes’s revival of Kanin’s play just opened, and you’ll see that — as well as a whole lot more.

Before going any further, it is worthwhile to point out that this is a larger achievement than a cursory examination might suggest. After all, Vanda and Billie are shockingly similar, and you may think it’s but a minor leap from one to the next. Both are actresses (current or recovering) who latch onto men who want to chain them to one role while they may be ideally suited to another. Both begin oblivious, but gradually become imposing personalities that force their men — and you — to trash your expectations and view them as much more than the “dumb broads” their foregoing reputations indicate. And both, in accordance with their predefined stature, are experts at using every last one of their feminine wiles to get what they want.

But Arianda created the alluring goddess Vanda; for over 60 years, Billie has been the exclusive property of a more tangible theatrical deity: Judy Holliday. That actress and comedienne originated Billie in 1946 and also preserved the role in (and won an Oscar for) the 1950 film, leaving behind a turn of surprising sensitivity and eccentricity that has ever since defined the role (and, for that matter, Holliday). Other actresses have rented the part from time to time: Madeline Kahn in the 1989 Broadway revival, Melanie Griffith in a 1993 Hollywood remake. But none has left the same indelible stamp.

Whether Arianda will remains to be seen, but she’s off to an astounding start. Her portrayal gingerly echoes Holliday’s, but doesn’t copy it. Arianda, for whom the word “statuesque” could well have been coined, provides a smokier sultriness and a harder innocence, which help establish an even more credible baseline for her transformation from bimbo to power player. Never, even in the earliest scenes, does she let her brutish sugar daddy, junk tycoon Harry Brock (Jim Belushi), who’s brought her to Washington, D.C. on a months-long trip to bribe a certain senator, unleash an unanswered pointed word. A furrowed-brow glare, the tiniest twist of her teasingly bulbous lips, or the right squeak of her voice, and it’s clear that — at least on some level — they’re already equals.

So when Harry convinces New Republic journalist Paul Verrall (Robert Sean Leonard) to “show her the ropes,” and make her easier to pass off in D.C.’s puffed political society, you get no sense that this is an impossible task. Even so, Arianda does not instantly give up the goods. Donning stylish satin pajamas (courtesy of costume designer Catherine Zuber) and bookworm glasses, she becomes every bit the uncertain intellectual, lost in an ever-expanding world that previously extended no further than her own manicured fingertips. Arianda approaches all these developments with an air of cautious wonder that is the finest-imaginable human approximation of a flower blooming in ultra-slow motion. And when she’s grown enough to take over, no hint of the earlier stepped-on girl remains. If you didn’t know, you’d swear the two Billies were played by different people.

If Arianda is the brightest pleasure of this production, she’s not the only one. Hughes presides over a sharp and funny rendering of Kanin’s play, the frankness and acidity of which may surprise you if all you know is the toned-down film. Though a few arid patches do slip through, particularly when Billie is not at the center of the action, Hughes’s production is funny, warm, and biting as an indictment of governmental graft and the cruelty of underestimation alike. Its messages about how big business and big government collude against the little guy — whom they think as far littler than he (or she) may actually be — still seems hauntingly relevant. John Lee Beatty’s set stops short of the ostentatious, high-luxury-duplex hotel suite that would most clearly paint Harry as undeserving nouveau riche, but is nonetheless a crisp and elegant backdrop for this refashioned Galatea story.

Belushi is excellent as Harry: down and dirty, and believably violent, but with a core of love that nonetheless justifies Billie’s leaving the chorus for him. Terry Beaver, as the on-the-take senator, and Frank Wood, as Harry’s mastermind lawyer, offer sterling support. Only Leonard disappoints, and only a little: It’s nice to see him back onstage after years on the TV show House, but he’s stiffer than he should be, presenting only flashes of the fire that could credibly inspire Billie to new heights of personal betterment. Paul should be more of a crusader and less of a passive literary activist; Leonard played the latter, to Tony-winning effect, in Tom Stoppard’s The Invention of Love, but it’s a shakier approach here.

There’s nothing flimsy about Arianda, who owns the stage — and your heart — every moment she’s on view. The bobble-headed intensity she brings to a marathon gin game against Harry (whom she wallops, by the way), the tenderness with which she clutches a torn-apart book she’s learned to appreciate, and the bear-trap ferocity she uses to defend herself when Harry tries to shove her back into a role she can no longer fill are all memorable evocations of both a woman determined to show there’s nothing she can’t do and the extraordinary star-in-the-making playing her. Perhaps Holliday and her legacy will remain intact in the wake of Arianda’s ministrations in this Born Yesterday, and other actresses at awards time may shiver in their shoes. But audiences daring to sample this sparkling new take on the Billie they thought they knew will have nothing at all to fear.